Singularly Perturbed Elliptic Dirichlet Problem with Three-band Boundary Layer

Abstract

Abstract. A singularly perturbed elliptic problem with Dirichlet boundary conditions is considered in the case of multiple roots of the degenerate equation. A three-zone boundary layer arises in the vicinity of the domain boundary with a different scale of boundary-layer variables and a different behaviour of the solution in different zones. The asymptotic expansion of the solution being in fractional powers of the small parameter, boundary-layer series are constructed using a non-standard algorithm. A complete asymptotic expansion of the solution is constructed and justified.

Keywords

• singularly perturbed elliptic equation
• case of multiple root of the degenerate equation
• asymptotic expansion of boundary layer type solution
• three-band boundary layer